6.4 Discussion
6.4.1 Comparison with literature
Body mass increased almost linearly during the observation period. This result is in agreement with other growth studies on humans (age: 5–12 years (Bénardet al.,2011)), rabbits (age: 14–126 days (Masoud et al., 1986)), and rats (age: 19–79 days (Bhaskar et al.,1950;Hansson et al.,1972)). Age-dependent morphometric measurements of the muscle-tendon complex during normal growth are rare, and there are only a small number of studies examining rabbits (Böl et al., 2016;Crawford,1950, 1954). The majority of research was performed on other species. To enable comparison with humans and rats as well as with deviating observation periods, growth data were normalised to the ages (tfg) when skeletal growth is almost complete (rattfg: about 100 days ; rabbittfg: about 120 days (Masoudet al.,1986); human tfg: about 17 years (Gindhart,1973)). Accordingly, data in this study comprise a growth period of 0.15tfg (18 days) to 0.9tfg (108 days).
Few studies have examined the same muscles analysed in the present study or provided geometric data to make subsequent comparisons. Increases in muscle belly and aponeurosis length of GM and TA were expected based on previous work (Crawford, 1954;Heslinga & Huijing,1990;Woittiezet al.,1986). Crawford(1954) observed changes in the TA muscle length of rabbits during growth. They marked the muscles of five young rabbits (35 days, 0.29tfg) in the longitudinal direction using thin steel wires at fixed intervals. They measured segmental length changes after about 119 days (0.99tfg).
The experiments showed that longitudinal growth occurred fairly evenly throughout the length of the muscle belly. They found very large interindividual differences in muscle growth, and the distance between the most distal and most proximal markers increased by about 35% and 80% for two different animals. For a conformable time period (35–108 days), a higher and more consistent increase in the whole muscle belly length (87%) was found in the present study.
The GM muscle belly length of children increased from 5 years (0.28tfg) to 12 years (0.71 tfg) by 47% (Bénardet al.,2011), which is in agreement with the increase of 53%
for rabbit GM in the present study within the same normalised observation period.
Almost equal growth also appeared for the aponeurosis length of human GM (55%
(Bénard et al., 2011)) and rabbit GM (65%) within this time period (0.28–0.71 tfg).
Heslinga & Huijing (1990) measured the aponeurosis length of rat GM at ages of 70 days (0.7tfg) and 98 days (0.98tfg). The reported increase in aponeurosis length (19%) was also similar to that of rabbit GM (24%) within the observed time period.
Larger differences occurred for the GM fascicle length of different species. Bénard et al.(2011) found an increase in human GM fascicle length of 5% per year. In contrast, almost no changes were observed in the GM fascicle length during growth in the present study (Figure 6.7), which is in agreement with observations of rat GM (Heslinga &
Huijing,1990). Thus, an increase in GM muscle mass (Figure6.2) resulted in an exclusive increase in CSA (see Eq. 6.1) of 12.2%/day. Slightly lower CSA growth rates were reported for rabbit EDL (9.5%/day) and SOL (7.7%/day) (Bölet al.,2016). As the GM fascicle length (Figure6.7) and pennation angle (meanα = 22.7°±3.6°, Table 6.1) did not change considerably for the age range studied, it is concluded that growth-related increases in muscle belly length are mainly explained by an increase in aponeurosis length, which is related to muscle fibre hypertrophy (Bénard et al., 2011). Heslinga &
Huijing (1990) provide a detailed discussion of the influence of increased aponeurosis length and CSA with unchanged muscle fascicle length.
Almost similar aponeurosis areas were found for GL and GM, which feature two explicitly pronounced tendon-aponeurosis structures on their proximal and distal ends (Figure 6.5). This has also been reported for rabbit SOL, EDL, and PLA (Böl et al., 2016). It is reasonable for the areas and growth ratios of distal and proximal aponeuroses to be similar because at both muscle ends, the same generated forces are transferred over the aponeurosis to the tendon. Furthermore, the number of muscle fibres connected to each aponeurosis should be the same.
Bölet al. (2016) performed the only study available on changes in aponeurosis area during growth. For rabbits between 18 and 108 days old, they measured the aponeurosis length, width, and area of the SOL, EDL, and PLA. In general, they reported a higher
6.4. DISCUSSION
growth rate of the aponeurosis length compared to its width, which is in agreement with our observations on GL, GM, FDL, and TA, as shown in Figure 6.5. However, when normalising the distal aponeurosis growth rates to the initial values, the aponeurosis growth was higher in the width (this study: 1.9 ± 0.3%/day; Böl et al. (2016): 2.6
± 0.7%/day) than in the length (this study: 1.5± 0.3%/day; Böl et al. (2016): 1.7 ± 0.2%/day). This might result from the muscle hypertrophy associated with a pronounced increase in muscle belly width, which is obvious for GL and GM in Figure6.3A and B.
Even though the muscle belly growth is more uniform in FDL and TA (Figure6.3C, D), the distal aponeurosis growth in the width (FDL: 2.0%/day; TA: 1.4%/day) is slightly higher than that of the length (FDL: 1.8%/day; TA: 1.1%/day). In contrast, normalised proximal aponeurosis growth is higher in length (1.6 ± 0.3%/day) than in width (1.2
±0.4%/day), cf. Table 6.2, indicating that there are factors other than the increase in muscle belly width affecting aponeurosis growth.
The physiological CSAs of GL, GM, FDL, and TA were smaller than their corresponding aponeurosis areas, as shown in Figure 6.4. This was also found for rabbit SOL, EDL, and PLA (Böl et al., 2016). Heslinga & Huijing (1990) explain this based on a two-dimensional approach. In principle, the appearance of a pennation angle between a muscle fibre and an aponeurosis segment requires a longer aponeurosis segment length compared to the muscle fibre diameter due to mechanical considerations. The muscle hypertrophy induced by an increase in fibre diameter may lead to an increase in pennation angle without adaption of the length of the aponeurosis segment (Heslinga &
Huijing,1990). Another mechanism may be the increase in aponeurosis segment length due to an increased muscle fibre diameter without changes in the pennation angle. For all the muscles observed, we found an obvious increase in aponeurosis length, as shown in Figure6.5.
The pennation angle of GM, FDL, and TA hardly changed from the youngest to the oldest animal (Table 6.1). This implies that the increase in fibre and fascicle diameters during muscle hypertrophy can only be accommodated by a simultaneous
and proportional increase in the aponeurosis length. Moreover, an additional increase in the GL pennation angle during growth (Table6.1) may further compensate for excessive hypertrophy. In fact, GL exhibits higher CSA compared to GM (Figure 6.5), although both muscles have similar aponeurosis areas. Thus, the lower aponeurosis-CSA ratio rACSAof GL (1.2) compared to GM (1.44) might be explained by the increasing pennation angle of GL and higher growth rate in GL muscle mass, as shown in Figure 6.2.
The lowest increase in CSA (4.8%/day) was found for TA. GL exhibited a growth rate that was almost three times higher (13.7%/day). This difference can be explained by the pronounced growth in the TA fascicle length (Figure6.7) compared to the almost equal fascicle lengths of GL as well as the higher increase in GL muscle mass (Figure 6.2). The CSA growth rates observed for SOL (7.7%/day) and EDL (9.5%) byBölet al.
(2016) are in between the values determined for TA and GL (Table 6.2).
In contrast to the limited number of age-dependent experimental analyses, studies on rabbit muscles at particular ages are more common (Böl et al., 2013; Hiepe et al., 2014; Lieber & Blevins,1989; Schenk et al., 2013; Siebert et al., 2015). These studies analysed muscle geometry as well as active and passive muscle properties from primarily adult specimens. However, it is possible to compare these results with the geometric data determined at discrete points. For example,Lieber & Blevins(1989) examined the muscle fibre architecture of 29 muscles of six rabbits with a mean mass of 2.5 ± 0.2 kg (which roughly corresponds to an age of 73 days with respect to the present study). In accordance with our study, muscles were fixed at knee and ankle joint angles of 90° for architectural determination. Their results regarding muscle belly dimensions, fascicle lengths, and pennation angles of GL, GM, FDL, and TA were compared with our results from analysing the 3D muscle architecture of a 70-day-old rabbit (m = 2.35 kg), as shown in Table6.3. In general, our data are consistent with the results fromLieber & Blevins (1989). Deviations in the pennation angle (10° and 8° for GM and TA, respectively) might partially reflect variations in ankle and knee joint angles or might be induced by differences in the observation method. Lieber & Blevins (1989) measured geometrical
6.4. DISCUSSION
parameters in local regions of the muscle surface, whereas mean values from the complete 3D fascicle architecture of the muscles were determined within the present study.
Parameter Muscle This Study Lieber & Blevins (1989)
Animal mass [kg] 2.35 2.5 ± 0.2
Muscle belly length [mm] GL 52.7 57.5 ± 2.9
GM 58.6 61.2 ± 2.9
FDL 48.0 51.2 ± 2.1
TA 55.6 56.9 ± 4.5
Fascicle length [mm] GL 14.2 ± 2.3 16.1 ± 0.8 GM 13.1 ± 2.0 14.7 ± 0.7 FDL 12.9 ± 3.9 12.4 ± 0.5 TA 31.7 ± 6.5 38.1 ± 3.0 Pennation angle [°] GL 17.5 ± 4.1 15.5 ± 3.0 GM 24.6 ± 3.4 13.8 ± 1.7 FDL 15.0 ± 3.2 14.5 ± 3.0 TA 11.3 ± 3.2 3.0 ± 1.0
Table 6.3: Comparison of the present results with muscle architectural parameters of rabbits with a given animal mass of 2.5 ± 0.2 kg provided by Lieber & Blevins (1989).
However, fascicle lengths were determined at a fixed ankle joint angle of 90°, similar toLieber & Blevins(1989). Changing the ankle angle might influence the results due to increase of the muscle lever arms. Based on geometrical calculation of the muscle-tendon complex lengths for ankle joint angles of 80° and 100°, using the measured muscle lever arms (see Figure 6.2), we found an additional increase and decrease in GL and GM fascicle lengths of + 1 mm and – 1 mm during the growth period, which would have a small influence on the results, as shown in Figure 6.7. Due to the smaller lever arm lengths, the influence on the FDL and TA fascicle lengths was < 0.2 mm.
The calculations were done under the assumption that length changes in the passive muscle-tendon complex induced by changing the ankle angle would primarily influence the fascicle length due to the higher compliance of passive muscle tissue compared to
the aponeurosis and tendons (Zuurbier et al.,1994). We conclude that changes of the ankle angle of about ± 10° during fixation of the preparation are negligible for fascicle length determination.
6.4.2 Functional relevance of changing tendon–muscle fascicle length ratio
It is well known that muscles have different tendon–muscle fascicle length ratios (rTFL), depending on the muscle function (Biewener, 1998; Biewener & Roberts, 2000; Mörl et al., 2016). Muscles that act as springs in bouncing gates and contribute to energy conservation have long SECs and short muscle fibres, which result in high rTFL. One typical example is the PLA (rTFL=18.7 (Biewener,1998)) of the wallaby, a muscle that is well adapted to spring-like energy storage and economical muscle force generation during hopping (Biewener & Baudinette,1995;Bieweneret al.,2004). In contrast, muscles that primarily act as motors in concentric contractions have a comparably short SEC and long muscle fibres. One example is the pigeon pectoralis (rTFL = 0.4), which shortens substantially during the downstroke to produce mechanical power for aerodynamic lift and thrust during flying (Biewener,1998).
For the adult GM and GL, an intermediate rTFL of 8 was observed, which is similar to that of horse M. gastrocnemius (rTFL = 8.7 (Biewener, 1998)) and slightly lower than that of camel M. gastrocnemius (rTFL = 11 (Alexander et al., 1982)). The gastrocnemii of horses and camels have more universal functions during locomotion that involves spring- and motor-like behaviour, as well as the capability of economical force production (Biewener, 1998). Based on the intermediate rTFL value, there might be a similar functional relevance of rabbit GL and GM. However, no kinematic study has examined rabbit hind-limb muscle function during locomotion. As shown in Figure 6.9, rTFL is low for muscles that act as motors, like the M. biceps femoris of wallabies (Biewener & Baudinette,1995), or for muscles that act as brakes, like M. vastus lateralis, which absorbs energy during the stance phase of walking, trotting, or galloping in rats
6.4. DISCUSSION
(Gillis & Biewener, 2001). Rabbit TA muscle exhibited a low rTFL of 2, indicating a similar functional relevance. In fact, the TA acts as both a motor (by dorsiflexion of the ankle joint in the swing phase) and a brake (by energy absorption in the early stance phase) during human locomotion (Ferris et al., 2005; Hamner et al., 2010).
Interestingly, rTFL was not a constant geometrical property of the specific muscle
Figure 6.9: Tendon–muscle fascicle length ratios (rTFL) of different adult mammalian muscles from the literature categorised by body mass. Changes inrTFL with increasing body mass (from 0.4 to 3.5 kg) determined in the present study and byBölet al.(2016) are shown by black and grey arrows, respectively. Muscles act as motors (*) or springs (†) during locomotion (Biewener,1998).
but instead changes during growth, as shown in Figure 6.8. We found an increase in rTFL by a factor of 2 (GL, GM, FDL) and even a slight decrease (TA). An increasing rTFLwas also reported for other rabbit shank muscles. During growth,rTFLof the SOL and PLA increased from 4 to 6 and from 8 to 18, respectively (Böl et al., 2016). The increase might indicate increasing importance of economical locomotion during growth (Bölet al.,2016). The metabolic cost of transport decreases with increasing body mass in various mammalian species (Tayloret al.,1970). Furthermore, an increasingrTFLwas reported for several shank muscles from 35 quadrupedal species ranging in body mass from 0.04 to 545 kg (Pollock & Shadwick, 1994). For instance, rTFL of the PLA and GAS respectively increased 3-fold and 15-fold over the observed body mass range. These arguments indicate that increasing the capacity of strain energy storage with increasing body mass might be relevant for not only the consideration of different species but also for better understanding of the changing energetics and potentially increased economical locomotion during growth.
6.4.3 Impact on muscle modelling
From a modelling perspective, the data presented are of great interest as they support appropriate model validation and thus contribute to more meaningful model concepts.
Besides the determined growth kinetics of the muscle bellies, aponeuroses, and tendons, the 3D fascicle data in particular allow for proper validation of 3D constitutive growth models. In turn, these models can be used to address functional relevance of structural changes during growth and how these changes are related to mechanical properties, which is largely unknown (Bénard et al., 2011). Furthermore, with conclusive growth model approaches at hand, load transfer mechanisms such as those determined experimentally byBöl et al.(2015) could be analysed and predicted in the future. Hence, the extensive datasets of the present study and the one provided byBölet al.(2016) are the first steps to developing and validating comprehensive growth models for the prediction of muscle development under various boundary conditions.